Question

Given the graphs of $f\left(x\right)=x^2\&g\left(x\right)=(kx{)}^2.$ The possible value of $k$ is

• A. $k=1$
• B. $k>1$
• C. $0<k<1$

Answer 1

The correct option is B $k>1$

From the given graph of $f\left(x\right)=x^2$ and $g\left(x\right)=(kx{)}^2$ as shown:

We know from the concept of horizontal stretching and shrinking of a graph that for any function $p\left(x\right),$ the graph of $p\left(kx\right),k>1$ will result in the the shrinking of graph horizontally, meanwhile for $0<k<1$ the graph will stretch horizontally.
Here, $g\left(x\right)$ results from horizontal shrinkage of $f\left(x\right)$
$\Rightarrow k>1$